Question

If log_α8 = γ, log_βα = –1 and log_1/4β = –1 then `(1/α + 1)^(log_sqrt(5)(β^2 + 4γ^2)` is equal to ______.

पर्याय

• `sqrt(5)`

• 5

• 25

• 625

Answer 1

If log_α8 = γ, log_βα = –1 and log_1/4β = –1 then `(1/α + 1)^(log_sqrt(5)(β^2 + 4γ^2)` is equal to 625.

Explanation:

log_α8 = γ, log_βα = –1, log_1/4β = –1

⇒ β = 4, α = `1/4`, γ = `-3/2`

⇒ `(1/α + 1)^(log_sqrt(5)(β^2 + 4γ^2)) = 5^(log_sqrt(5)(16 + 9)`

= `5^(log_(5 1/2) 5^2)`

= 5⁴

= 625